Geodesic

Geodesic (pronounced jee-uh-des-ik or jee-uh-dee-sik)

(1) In spherical geometry, a segment of a great circle.

(2) In mathematics, a course allowing the parallel-transport of vectors along a course that causes tangent vectors to remain tangent vectors throughout that course (a straight curve, a line that is straight; the shortest line between two points on a specific surface).

1821: A back-formation from geodesy (a branch of science dealing with the measurement and representation of Earth, its gravitational field and geodynamic phenomena (polar motion, Earth tides, and crustal motion) in three-dimensional, time-varying space and with great (and "down-to-earth" as it were) practical application in surveying.  The adjectives geodesical & geodetic had first appeared in 1818 & 1819 respectively, both from geodetical which had been in use since the early seventeenth century.  All the forms are derive ultimately from the Ancient Greek γεωδαισία (geodaisía) from γῆ (geo) (earth) + δαιεῖν (daiesthai) ("to divide" or "to apportion") and the use in English was most influenced by the French géodésique, dating from 1815.  In general use, the word entered general use after 1953 when it was used of the "geodesic dome" (a structure built according to geodesic principles); despite the earlier use in wartime aircraft construction, the use there was only ever "engineer's slang".    Geodesic is a noun & adjective, geodesicity is a noun, geodesical is an adjective and geodesically is an adverb; the noun plural is geodesics.    The alternative adjectival form geodetic appeared in 1834 but fell from use by mid-century.  

Four-dimensional space-time.

Geodesic describes the curve that locally minimizes the distance between two points on any mathematically defined space, such as a curved manifold; essentially the path is the one of the most minimal curvature so, in non-curved three-dimensional space, the geodesic is a straight line.  Under Albert Einstein's (1879-1955) theory of general relativity (1915), the trajectory of a body with negligible mass on which only gravitational forces are acting (ie a free falling body), defines the geodesic in curved, four-dimensional spacetime.  Dictionaries and style guides seem to prefer “space-time” but scientists (and space nerds) like “spacetime” and because it was one of them who “invented it”, it seems polite to ignore the hyphen.  The term, a calque of the German Raumzeit (the construct in English being (obviously) space + time) first appeared in a paper by German mathematician Hermann Minkowski (1864–1909), published in the Philosophical Review.  The existence of the noun plural "spacetimes" does not imply something to do with the so-called multiverse (in cosmology, a hypothetical model in which simultaneously more than one universe exists) but rather that there are different space-times created in different places at different times.

General relativity fan girl Lindsay Lohan in optical illusion dress from the Autumn-Winter collection of interior designer Matthew Williamson (b 1971), illustrating an object causing the curvature of spacetime, Gift Global Gala, Four Seasons hotel, London, November 2014.  An “optical illusion dress” is one which uses a fabric print or other device to create the effect and differs from an “illusion dress” which is made with skin-tone fabrics placed to emulate the wearer’s own flesh.

In Einstein's theory of general relativity, gravity is treated not as a force as had been the historic understanding explained in the writings of Sir Isaac Newton (1642–1727) but rather as a curvature of spacetime caused by the presence of mass and (thus) energy.  The Sun, being a massive object, causes a (relatively) significant curvature in the surrounding spacetime and the Earth, as it moves through this curved spacetime, follows a path (a geodesic) which manifests as what appears to be an “orbit” around the Sun.  It is this curvature of spacetime that is perceived as the “gravitational pull” of the Sun on the Earth, keeping it in a (relatively) stable and predictable orbit.  Einsteinian physics supplanted Newtonian physics as the structural model of the universe and nothing has since been the same. 

Hull of Vickers R.100 Airship.

Sir Barnes Wallis (1887-1979) was an English engineer, best remembered as the inventor of the bouncing bomb used by the Royal Air Force in Operation Chastise (dubbed the "Dambusters" raid) to attack the Ruhr Valley dams during World War II and the big Tallboy (6 tonnes) and Grand Slam (10 tonnes) deep-penetration "earthquake" bombs.  Wallis had been working on the Admiralty’s R.100 airship when he visited the Blackburn aircraft factory and was surprised to find the primitive wood-and-canvas methods of the Great War era still in use, a notable contrast to the elegant and lightweight aluminum structure of airships.  He was soon recruited by Vickers to apply his knowledge to the new generation of fixed-wing aircraft which would use light alloy construction for the internal structure.  His early experience wasn’t encouraging, the first prototype torpedo bomber, which used light alloy wing spars inspired by the girder structure of R.100, breaking up mid-air during a test-flight.  Returning to the drawing board, Wallis designed a revolutionary structural system; instead of using beams supporting an external aerodynamic skin, he made the structural members form the aerodynamic shape itself.

The geodesic structure in an airframe.

The principle was that the members followed geodesic curves in the surface, the shortest distance between two points in the curved surface although he only ever referred to it in passing as geodetic; it wouldn’t be until later the label came generally to be applied to the concept.  As a piece of engineering, it worked superbly well, having the curves form two helices at right angles to one another, the geodetic members became mutually supporting, rendering the overall framework immensely strong as well as comparatively light.  Revolutionary too was the space efficiency; because the geodetic structure was all in the outer part of the airframe meant that the centre was a large empty space, ready to take payload or fuel and the inherent strength was soon proven.  While conducting the usual wing-loading stress tests to determine the breakage point, the test routine was abandoned because the wings couldn’t be broken by the test rig.

Vickers Wellseley.

The benefits inherent in the concept were soon demonstrated.  Vickers’ first geodesic aircraft, the Wellesley, entered service in 1937 and in 1938, three of them, making use of the massive fuel capacity the structure made possible, flew non-stop from Ismailia in Egypt to Darwin in Australia, setting a new world record distance of 7,158 miles (11,265 km), an absolute record which stood until broken in 1946 by a Boeing B-29 Superfortress; it remains to this day the record for a single-engined aircraft with a piston engine, and also for aircraft flying in formation.  While the Wellesleys were under construction, Wallis designed a larger twin-engined geodetic bomber which became the Vickers Wellington, the mainstay of the RAF’s Bomber Command until 1943 when the new generation of four-engined heavy bombers began to be supplied in in the volume needed to form a strategic force.  Despite that, the Wellington was still used in many roles and remained in production until after the end of hostilities.  Over eleven-thousand were built and it was the only British bomber to be in continuous production throughout the war.

Vickers Wellington fuselage internal detail.

The final aircraft of the type, with a more complex geodetic structure was a four-engined heavy bomber called the Windsor but testing established it didn’t offer significantly better performance than the heavies already in service, and the difficulties which would be caused by trying to replicate the servicing and repair infrastructure was thought too onerous so it never entered production.  Post-war, higher speeds and operating altitudes with the consequent need for pressurised cabins rendered the fabric-covered geodetics obsolete.

Aston Martin DB4 GT Zagato (one of 19 in the "Continuation Series", production of which began in 2019) during construction, an aluminium panel being attached to the superleggera frame, Aston Martin Works, Newport Pagnell, Buckinghamshire, England.

There are obvious visual similarities between the classic superleggera method and the geodesic structure used in airframes and some buildings, most famously the “geodesic dome”.  The imperatives of both were strength both aim to create strong and lightweight structures, but they differ in their specific design and application.  As used in airframes, the geodesic structure consisted of a network of intersecting diagonal braces, creating a lattice framework which distributed loads as evenly as possible while providing a high strength-to-weight ratio.  This was of great significance in military airplanes used in combat because it enhanced their ability better to withstand damage better, the stresses distributed across the structure rather than being restricted to a limited area which could create a point-of-failure.  The geodesic framework was based on geometric principles which had been developed over centuries and typically employed hexagons & triangles to render a structure which was both rigid & light.  Superleggera construction differed in that it involves the creation of a lightweight tubular frame, covered with aluminum body panels of a thinness which wouldn’t have been possible with conventional engineering.  The attraction of the superleggera technique was the (relatively) minimalistic framework supported the skin, optimizing weight reduction without compromising strength.  So, structurally, the difference was the geodesic design used a network of intersecting braces to form a lattice, while the superleggera construction used a tubular frame covered with panels.